There was one thing wrong with the $500 million settlement in the CityTime scandal: the timing.

SAIC, the company chiefly responsible for building the corruption-infused timekeeping system, agreed to the extraordinary payment last week to avoid criminal prosecution by US Attorney Preet Bharara.

As luck would have it, the announcement came just as Mayor Bloomberg is gearing up for budget negotiations with the City Council.

All of a sudden, council members clamoring for restorations to child care, libraries and other programs cut by the mayor as part of the ridiculous budget maneuvers that take place every year see dollar signs before their eyes.

The council’s Women’s Caucus is demanding that the administration “take this opportunity to make a sound investment in our city’s children and working families.”

“This unexpected money makes it possible for the mayor to restore child care and after-school programs to 47,000 children,” proclaimed the Campaign for Children advocacy group.

Councilwoman Tish James (D-Brooklyn) proposed allocating part of the CityTime windfall to $113 million in unfunded kids’ programs.

The extra cash is bound to put added pressure on the mayor to spend more now.

“People think when there’s more money, it’s easier to do the budget,” said one insider. “I think it makes it harder.”

The way the budget game gets played is that the mayor threatens to cut services worth in the vicinity of $300 million to $400 million that he knows the council will put back.

The money is hidden away in budgetary caves, and miraculously appears to save the day in late May or early June, when both sides usually come together.

But now there’s an extra $466 million to contend with, the refund coming to the city from the $500 million SAIC sent to the US Attorney’s Office.

Bloomberg insists that the city’s share of the payout is all spoken for.

“This money was spent a long time ago,” he said, moments after Bharara announced the settlement.

On his radio show Friday, he went so far as to allocate it.

“We have a $3 billion deficit projected for the [fiscal] year 2014,” the mayor said. “Now we have a $2.5 billion deficit unless our tax revenues don’t come up to what we’re thinking, in which case it may be even bigger.”

Domenic Recchia (D-Brooklyn), the council’s finance chairman, said he’s sympathetic to the spend-it-now views, but said, “We have to plan for the future, and next year’s budget is going to be tough.”